U.S. patent number 9,927,510 [Application Number 14/819,649] was granted by the patent office on 2018-03-27 for star tracker.
This patent grant is currently assigned to The Charles Stark Draper Laboratory, Inc.. The grantee listed for this patent is The Charles Stark Draper Laboratory, Inc.. Invention is credited to Gregory P. Blasche, Murali V. Chaparala, Robin Mark Adrian Dawson, Juha-Pekka J. Laine, Benjamin F. Lane, Stephen P. Smith, Erik L. Waldron.
United States Patent |
9,927,510 |
Waldron , et al. |
March 27, 2018 |
Star tracker
Abstract
A star tracker determines a location or orientation of an
object, such as a space vehicle, by observing unpolarized light
from one or more stars or other relatively bright navigational
marks, without imaging optics, pixelated imaging sensors or
associated pixel readout electronics. An angle of incidence of the
light is determined by comparing signals from two or more
differently polarized optical sensors. The star tracker may be
fabricated on a thin substrate. Some embodiments have vertical
profiles of essentially just their optical sensors. Some
embodiments include micro-baffles to limit field of view of the
optical sensors.
Inventors: |
Waldron; Erik L. (Concord,
MA), Laine; Juha-Pekka J. (Boston, MA), Blasche; Gregory
P. (Burlington, MA), Chaparala; Murali V. (Newton,
MA), Dawson; Robin Mark Adrian (Waltham, MA), Lane;
Benjamin F. (Grafton, MA), Smith; Stephen P. (Acton,
MA) |
Applicant: |
Name |
City |
State |
Country |
Type |
The Charles Stark Draper Laboratory, Inc. |
Cambridge |
MA |
US |
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Assignee: |
The Charles Stark Draper
Laboratory, Inc. (Cambridge, MA)
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Family
ID: |
55267262 |
Appl.
No.: |
14/819,649 |
Filed: |
August 6, 2015 |
Prior Publication Data
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Document
Identifier |
Publication Date |
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US 20160041265 A1 |
Feb 11, 2016 |
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Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
Issue Date |
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62033961 |
Aug 6, 2014 |
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
G01C
3/085 (20130101); G01S 3/7867 (20130101) |
Current International
Class: |
G01C
21/02 (20060101); G01S 3/786 (20060101); G01C
3/08 (20060101) |
Field of
Search: |
;250/203.6
;348/135,139-140,169-171 |
References Cited
[Referenced By]
U.S. Patent Documents
Foreign Patent Documents
Other References
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spotted-in-cosmic-microwave-background, 3 Pages, Jul. 25, 2013.
cited by applicant .
Chu, et al., "Design of a Novel Polarization Sensor for
Navigation," Proceedings of the 2007 IEEE International Conference
on Mechatronics and Automation, 6 Pages, Aug. 5-8, 2007. cited by
applicant .
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Robot Navigation," Proceedings of the 2009 IEEE International
Conference on Mechatronics and Automation, 6 Pages, Aug. 9-12,
2009. cited by applicant .
DePoy, "The Magnitude Scale--Measuring the brightness of
astronomical objects," 35 Pages, Sep. 8, 2010. cited by applicant
.
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sky-polarimetric Viking navigation for north determination: a
planetarium experiment," Journal of the Optical Society of America,
vol. 31, No. 7, 12 Pages, Jul. 2014. cited by applicant .
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arXiv:astro-ph/0111253v1, 7 Pages, Nov. 13, 2001. cited by
applicant .
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starlight," Arkiv for Astronomi, Band 4, No. 22, 17 Pages, Oct. 26,
1966. cited by applicant .
Muhlschlegel, et al., "Resonant Optical Antennas," Science, vol.
308, 3 Pages, Jun. 10, 2005. cited by applicant .
Sarkar, et al., "Navigation Using CMOS Polarization Sensor,"
Springer, vol. 461, pp. 185-214, 2013 [Abstract]. cited by
applicant .
Schuller, et al. "Plasmonics for extreme light concentration and
manipulation," Nature Materials, vol. 9, pp. 193-204, Mar. 2010.
cited by applicant .
Tanemura, et al., "Multiple-Wavelength Focusing of Surface Plasmons
with a Non-periodic Nanoslit Coupler," Nano Letters, vol. 11, 6
Pages, 2011. cited by applicant .
Tang, et al., "Nanometre-scale germanium photodetector enhanced by
a near-infrared dipole antenna," Nature Photonics, vol. 2, pp.
226-229, 2008 [Abstract]. cited by applicant .
Wikipedia, "Cosmic microwave background,"
https://en.wikipedia.org/w/index.php?title=Cosmic_microwave_background&ol-
did=566944072, 14 Pages, Aug. 3, 2013. cited by applicant .
Wikipedia, "Nantenna,"
https://en.wikipedia.org/w/index.php?title=Nantenna&oldid=558319800,
7 Pages, Jun. 4, 2013. cited by applicant .
Wikipedia, "Polarization in astronomy,"
https://en.wikipedia.org/w/index.php?title=Polarization_in_astronomy&oldi-
d=543992427, 2 Pages, Mar. 14, 2013. cited by applicant .
Wikipedia, "Rectenna,"
https://en.wikipedia.org/w/index.php?title=Rectenna&oldid=560627000,
3 Pages, Jun. 19, 2013. cited by applicant.
|
Primary Examiner: Luu; Thanh
Assistant Examiner: Wyatt; Kevin
Attorney, Agent or Firm: Sunstein Kann Murphy & Timbers
LLP
Parent Case Text
CROSS REFERENCE TO RELATED APPLICATIONS
This application claims the benefit of U.S. Provisional Patent
Application No. 62/033,961, filed Aug. 6, 2014, titled "Star
Tracker," the entire contents of which are hereby incorporated by
reference herein, for all purposes.
Claims
What is claimed is:
1. A method for determining a direction to a source of unpolarized
electromagnetic radiation, the method comprising: exposing a first
sensor to the unpolarized electromagnetic radiation, the first
sensor being primarily sensitive to electromagnetic radiation
polarized along a first axis and configured to generate a first
signal proportional to a magnitude of the unpolarized
electromagnetic radiation detected by the first sensor; exposing a
second sensor to the unpolarized electromagnetic radiation, the
second sensor being primarily sensitive to electromagnetic
radiation polarized along a second axis, different than the first
axis, and configured to generate a second signal proportional to a
magnitude of the unpolarized electromagnetic radiation detected by
the second sensor; determining a ratio of the first signal to the
second signal; and using the ratio to calculate an angle of
incidence of the unpolarized electromagnetic radiation.
2. A method according to claim 1, wherein exposing the first and
second sensors to the unpolarized electromagnetic radiation
comprises exposing the first and second sensors to unpolarized
electromagnetic radiation from a star.
3. A method according to claim 1, further comprising: automatically
accessing a database that stores a star catalog; and automatically
calculating a location in space based at least in part on the angle
of incidence and information in the star catalog.
4. A method according to claim 1, further comprising: automatically
accessing a database that stores a star catalog; and automatically
calculating a direction to a star and identity of the star, based
at least in part on the angle of incidence and information in the
star catalog.
5. A method according to claim 1, wherein: exposing the first
sensor to the unpolarized electromagnetic radiation comprises
exposing a first array of nanoantennas to the unpolarized
electromagnetic radiation, wherein all nanoantennas of the first
array of nanoantennas are similarly oriented so as to be primarily
sensitive to electromagnetic radiation polarized along the first
axis, and all the nanoantennas of the first array of nanoantennas
are electrically coupled together to generate the first signal; and
exposing the second sensor to the unpolarized electromagnetic
radiation comprises exposing a second array of nanoantennas to the
unpolarized electromagnetic radiation, wherein all nanoantennas of
the second array of nanoantennas are similarly oriented so as to be
primarily sensitive to electromagnetic radiation polarized along
the second axis, and all the nanoantennas of the second array of
nanoantennas are electrically coupled together to generate the
second signal.
6. A method according to claim 1, further comprising: storing a
value representing the second signal; tilting the second sensor;
exposing the tilted second sensor to the unpolarized
electromagnetic radiation; and generating a third signal
proportional to a magnitude of the unpolarized electromagnetic
radiation detected by the tilted second sensor; wherein:
determining the ratio of the first signal to the second signal and
using the ratio to calculate the angle of incidence of the
unpolarized electromagnetic radiation comprises using the first
signal, the stored value representing the second signal and the
third signal to calculate the angle of incidence of the unpolarized
electromagnetic radiation.
7. A method according to claim 1, further comprising compensating
for a degree to which the unpolarized electromagnetic radiation is
polarized.
8. A method according to claim 1, wherein: exposing the first
sensor comprises providing a sensor comprising a plurality of first
elements, each element of the plurality of first elements being
configured to generate a signal proportional to electromagnetic
radiation incident upon the element; exposing the second sensor
comprises providing a sensor comprising a plurality of second
elements, each element of the plurality of second elements being
configured to generate a signal proportional to electromagnetic
radiation incident upon the element; the method further comprising:
automatically adjusting sensitivity of the plurality of first
elements, such that each element of the plurality of first elements
is preferentially sensitive to incident electromagnetic radiation
having a first polarization; and automatically adjusting
sensitivity of the plurality of second elements, such that each
element of the plurality of second elements is preferentially
sensitive to incident electromagnetic radiation having a second
polarization, different than the first polarization.
9. A method according to claim 8, wherein automatically adjusting
the sensitivity of the plurality of first elements and the
plurality of second elements comprises automatically adjusting the
sensitivity of the plurality of first elements and automatically
adjusting the sensitivity of the plurality of second elements, such
that the first polarization is at least approximately perpendicular
to the second polarization.
10. A star tracker for determining a direction to a source of
unpolarized electromagnetic radiation, the star tracker comprising:
a plurality of electromagnetic radiation sensors, wherein each
sensor of the plurality of electromagnetic radiation sensors is
primarily sensitive to electromagnetic radiation polarized along a
different axis and generates a proportional signal in proportion to
a magnitude of unpolarized electromagnetic radiation detected by
the sensor; a ratio detector that receives the proportional signals
generated by the plurality of electromagnetic radiation sensors and
generates a ratio signal that represents a ratio of at least two of
the proportional signals; and an angle of incidence calculator that
receives the ratio signal and generates therefrom a signal
representing an angle of incidence of the unpolarized
electromagnetic radiation.
11. A star tracker according to claim 10, further comprising: a
database that stores a star catalog; and a navigation calculator
that receives the angle of incidence signal, accesses the star
catalog and calculates an orientation or location in space based at
least in part on the angle of incidence signal and information in
the star catalog.
12. A star tracker according to claim 11, wherein: the star catalog
includes information about a degree of polarization of
electromagnetic radiation from at least one star; and at least one
of the ratio detector and the incidence angle calculator uses the
information about the degree of polarization of the electromagnetic
radiation from the at least one star to compensate at least one of
the ratio signal and the signal representing an angle of
incidence.
13. A star tracker according to claim 10, wherein each sensor of
the plurality of electromagnetic radiation sensors comprises an
array of similarly oriented nanoantennas, all oriented so as to be
primarily sensitive to electromagnetic radiation polarized along
the axis of the sensor and all electrically coupled together to
generate the proportional signal for the sensor.
14. A star tracker according to claim 10, wherein: at least one
sensor of the plurality of electromagnetic radiation sensors is
tiltable; the star tracker further comprising: a motor mechanically
coupled to the at least one tiltable sensor, so as to tilt the at
least one sensor from a first plane to a second plane; and wherein:
the at least one tiltable sensor generates at least a first portion
of the proportional signal, based on a magnitude of unpolarized
electromagnetic radiation detected by the at least one tiltable
sensor while the at least one tiltable sensor is in the first
plane, and the at least one tiltable sensor generates a second
portion of the proportional signal, based on a magnitude of
unpolarized electromagnetic radiation detected by the at least one
tiltable sensor while the at least one tiltable sensor is in the
second plane; and the ratio detector generates at least a first
portion of the ratio signal based on the first portion of the
proportional signal, and the ratio detector generates at least a
second portion of the ratio signal based on the second portion of
the proportional signal.
15. A computer program product for determining a direction to a
source of unpolarized electromagnetic radiation, the computer
program product comprising a non-transitory computer-readable
medium having computer readable program code stored thereon, the
computer readable program code, when executed by a processor,
causes the processor to: receive a first signal from a first sensor
exposed to the unpolarized electromagnetic radiation, the first
sensor being primarily sensitive to electromagnetic radiation
polarized along a first axis and configured to generate the first
signal proportional to a magnitude of the unpolarized
electromagnetic radiation detected by the first sensor; receive a
second signal from a second sensor exposed to the unpolarized
electromagnetic radiation, the second sensor being primarily
sensitive to electromagnetic radiation polarized along a second
axis, different than the first axis, and configured to generate the
second signal proportional to a magnitude of the unpolarized
electromagnetic radiation detected by the second sensor; determine
a ratio of the first signal to the second signal; and use the ratio
to calculate an angle of incidence of the unpolarized
electromagnetic radiation.
16. A computer program product according to claim 15, wherein the
computer readable program code further causes a processor to:
automatically access a database that stores a star catalog; and
automatically calculate a location in space based at least in part
on the angle of incidence and information in the star catalog.
17. A computer program product according to claim 15, wherein: the
first sensor is exposed to the unpolarized electromagnetic
radiation by exposing a first array of nanoantennas to the
unpolarized electromagnetic radiation, wherein all nanoantennas of
the first array of nanoantennas are similarly oriented so as to be
primarily sensitive to electromagnetic radiation polarized along
the first axis, and all the nanoantennas of the first array of
nanoantennas are electrically coupled together to generate the
first signal; and the second sensor is exposed to the unpolarized
electromagnetic radiation by exposing a second array of
nanoantennas to the unpolarized electromagnetic radiation, wherein
all nanoantennas of the second array of nanoantennas are similarly
oriented so as to be primarily sensitive to electromagnetic
radiation polarized along the second axis, and all the nanoantennas
of the second array of nanoantennas are electrically coupled
together to generate the second signal.
18. A computer program product according to claim 15, wherein the
computer readable program code further causes a processor to: store
a value representing the second signal; tilt the second sensor;
expose the tilted second sensor to the unpolarized electromagnetic
radiation; and generate a third signal proportional to a magnitude
of the unpolarized electromagnetic radiation detected by the tilted
second sensor; wherein: determine the ratio of the first signal to
the second signal and use the ratio to calculate the angle of
incidence of the unpolarized electromagnetic radiation comprises
using the first signal, the stored value representing the second
signal and the third signal to calculate the angle of incidence of
the unpolarized electromagnetic radiation.
19. A computer program product according to claim 15, wherein the
computer readable program code further causes a processor to
compensate for a degree to which the unpolarized electromagnetic
radiation is polarized.
20. A star tracker for determining a direction to a source of
unpolarized electromagnetic radiation, the star tracker comprising:
a first electromagnetic radiation sensor configured to generate a
first signal proportional to a first polarization component of
unpolarized electromagnetic radiation impinging on the first
electromagnetic radiation sensor; a second electromagnetic
radiation sensor configured to generate a second signal
proportional to a second polarization component of unpolarized
electromagnetic radiation impinging on the second electromagnetic
radiation sensor, the second polarization component being oriented
differently than the first polarization component; a ratio detector
that receives the first and second signals and generates a ratio
signal that represents a ratio of the first signal to the second
signal; and an angle of incidence calculator that receives the
ratio signal and generates therefrom a signal representing an angle
of incidence of the unpolarized electromagnetic radiation.
21. A star tracker, comprising: a plurality of electromagnetic
radiation sensors, each sensor of the plurality of electromagnetic
radiation sensors configured to generate a respective signal in
proportion to magnitude of a different polarization component of
unpolarized electromagnetic radiation impinging on the sensor; and
a ratio detector configured to receive the signals generated by the
plurality of electromagnetic radiation sensors and calculate an
angle of incidence of the unpolarized electromagnetic radiation.
Description
TECHNICAL FIELD
The present invention relates to star trackers and, more
particularly, to star trackers having polarized sensors, rather
than imaging optics.
BACKGROUND ART
Most artificial satellites, spacecraft and other craft such as
aircraft, ship and ground vehicles (collectively referred to herein
as vehicles) require information about their locations and/or
attitudes to accomplish their missions. This information may be
obtained from one or more sources, such as the global positioning
system (GPS), ground-based radar tracking stations and/or on-board
star trackers.
A star tracker is an optical device that measures angles to one or
more stars, as viewed from a vehicle. A star tracker typically
includes a star catalog that lists bright navigational stars and
information about their locations in the sky, sufficient to
calculate a location of a vehicle in space, given bearings to one
or more of the stars. A conventional star tracker includes a lens
that projects an image of a star onto a photocell, or that projects
an image of one or more stars onto a pixelated light-sensitive
sensor array (collectively, a digital camera). The lens typically
constitutes a large fraction of the mass of the star tracker. The
digital camera also typically constitutes a large fraction of the
electronics of the star tracker, and it consumes a significant
fraction of the electrical power consumed by the star tracker.
One type of star tracker is "strapped-down," meaning its view
angle, relative to its vehicle, is fixed. Another type of star
tracker can be aimed mechanically, such as in a direction in which
a navigational star is expected to be seen. Using data from the
photocell or sensor array, the star catalog and information about
the star tracker's view angle, relative to the vehicle, the star
tracker calculates a position of the vehicle in space.
Strap-down star trackers are mechanically simpler than mechanically
aimable (gimbaled) star trackers. However, the fixed view angle of
a strap-down star tracker limits the number of navigational stars
that may be used. Mechanically aimable star trackers can use a
larger number of navigational stars. However, aiming a star
tracker, relative to its vehicle, with the required precision,
poses substantial problems.
An ideal star tracker would be mechanically, electrically and
optically simple, small, low in mass and consume little power.
Jinkui Chu, et al., describe a polarization-based navigation system
for a mobile robot (Design of a Novel Polarization Sensor for
Navigation, Proceedings of the 2007 IEEE International Conference
on Mechatronics and Automation, Aug. 5-8, 2007, pp. 3161-3166,
Harbin, China and Application of a Novel Polarization Sensor to
Mobile Robot Navigation, Proceedings of the 2009 IEEE International
Conference on Mechatronics and Automation, Aug. 9-12, 2009, pp.
3763-3768, Changchun, China). However, the Chu device requires
incoming light to be at least fairly strongly polarized. Rayleigh
scattering of sunlight in the atmosphere causes polarization
patters in the sky, as observed from earth. The Chu device is
designed to operate on earth by observing these polarization
patters. Star light is essentially unpolarized, or only very
slightly polarized. The Chu device is, therefore, not useful as a
star tracker, particularly in space.
SUMMARY OF EMBODIMENTS
An embodiment of the present invention provides a method for
determining a direction to a source of unpolarized electromagnetic
radiation. The method includes exposing a first sensor to the
unpolarized electromagnetic radiation. The first sensor is
primarily sensitive to electromagnetic radiation polarized along a
first axis. The first sensor is configured to generate a first
signal proportional to a magnitude of the unpolarized
electromagnetic radiation detected by the first sensor. The method
also includes exposing a second sensor to the unpolarized
electromagnetic radiation. The second sensor is primarily sensitive
to electromagnetic radiation polarized along a second axis. The
second axis is different than the first axis. The second sensor is
configured to generate a second signal proportional to a magnitude
of the unpolarized electromagnetic radiation detected by the second
sensor. The method also includes determining a ratio of the first
signal to the second signal. An angle of incidence of the
unpolarized electromagnetic radiation is calculated using the
ratio.
Exposing the first and second sensors to the unpolarized
electromagnetic radiation may include exposing the first and second
sensors to unpolarized electromagnetic radiation from a star.
A database that stores a star catalog may be automatically
accessed. A location in space may be automatically calculated,
based at least in part on the angle of incidence and information in
the star catalog.
A database that stores a star catalog may be automatically
accessed. A direction to a star and identity of the star may be
automatically calculated, based at least in part on the angle of
incidence and information in the star catalog.
Exposing the first sensor to the unpolarized electromagnetic
radiation may include exposing a first array of nanoantennas to the
unpolarized electromagnetic radiation. All nanoantennas of the
first array of nanoantennas may be similarly oriented, so as to be
primarily sensitive to electromagnetic radiation polarized along
the first axis. All the nanoantennas of the first array of
nanoantennas may be electrically coupled together to generate the
first signal. Exposing the second sensor to the unpolarized
electromagnetic radiation may include exposing a second array of
nanoantennas to the unpolarized electromagnetic radiation. All
nanoantennas of the second array of nanoantennas may be similarly
oriented, so as to be primarily sensitive to electromagnetic
radiation polarized along the second axis. All the nanoantennas of
the second array of nanoantennas may be electrically coupled
together to generate the second signal.
The method may also include storing a value representing the second
signal and tilting the second sensor. The tilted second sensor may
be exposed to the unpolarized electromagnetic radiation. A third
signal may be generated proportional to a magnitude of the
unpolarized electromagnetic radiation detected by the tilted second
sensor. Determining the ratio of the first signal to the second
signal and using the ratio to calculate the angle of incidence of
the unpolarized electromagnetic radiation may include using the
first signal, the stored value representing the second signal and
the third signal to calculate the angle of incidence of the
unpolarized electromagnetic radiation.
The method may include compensating for a degree to which the
unpolarized electromagnetic radiation is polarized.
Sensing the electromagnetic radiation may include providing a
sensor that includes a plurality of elements. Each element of the
plurality of elements may be configured to generate a signal
proportional to electromagnetic radiation incident upon the
element. Sensitivity of at least one element of the plurality of
elements may be automatically adjusted, such that each element of
the plurality of elements is preferentially sensitive to incident
electromagnetic radiation having a respective polarization, wherein
at least two elements of the plurality of elements are
preferentially sensitive to different polarizations. Determining
the polarization direction of the electromagnetic radiation may
include calculating a ratio of signals generated by the at least
two elements of the plurality of elements.
Exposing the first sensor may include providing a sensor that
includes a plurality of first elements. Each element of the
plurality of first elements may be configured to generate a signal
proportional to electromagnetic radiation incident upon the
element. Exposing the second sensor may include providing a sensor
comprising a plurality of second elements. Each element of the
plurality of second elements may be configured to generate a signal
proportional to electromagnetic radiation incident upon the
element. The method may further include automatically adjusting
sensitivity of the plurality of first elements, such that each
element of the plurality of first elements is preferentially
sensitive to incident electromagnetic radiation having a first
polarization. The sensitivity of the plurality of second elements
may be automatically adjusted, such that each element of the
plurality of second elements is preferentially sensitive to
incident electromagnetic radiation having a second polarization.
The second polarization may be different than the first
polarization.
Automatically adjusting the sensitivity of the at least one element
of the plurality of elements may include automatically adjusting
the sensitivity of the at least one element, such that the at least
two elements of the plurality of elements are preferentially
sensitive to mutually perpendicular polarizations.
Automatically adjusting the sensitivity of the plurality of first
elements and the plurality of second elements may include
automatically adjusting the sensitivity of the plurality of first
elements and automatically adjusting the sensitivity of the
plurality of second elements, such that the first polarization is
at least approximately perpendicular to the second
polarization.
Another embodiment of the present invention provides a star tracker
for determining a direction to a source of unpolarized
electromagnetic radiation. The star tracker includes a plurality of
electromagnetic radiation sensors. Each sensor of the plurality of
electromagnetic radiation sensors is primarily sensitive to
electromagnetic radiation polarized along a different axis. Each
sensor generates a signal (a "proportional signal") in proportion
to a magnitude of unpolarized electromagnetic radiation detected by
the sensor. The star tracker also includes a ratio detector. The
ratio detector receives the proportional signals generated by the
plurality of electromagnetic radiation sensors. The ratio detector
generates a signal (a "ratio signal") that represents a ratio of at
least two of the proportional signals. The star tracker also
includes an angle of incidence calculator. The angle of incidence
calculator receives the ratio signal and generates therefrom a
signal representing an angle of incidence of the unpolarized
electromagnetic radiation.
The star tracker may also include a database that stores a star
catalog. The star tracker may also include a navigation calculator
that receives the angle of incidence signal. The navigation
calculator accesses the star catalog and calculates an orientation
or location in space, based at least in part on the angle of
incidence signal and information in the star catalog.
The star catalog may include information about a degree of
polarization of light or other electromagnetic radiation from at
least one star. The ratio detector and/or the incidence angle
calculator uses the information about the degree of polarization of
the light or other electromagnetic radiation from the at least one
star to compensate the ratio signal and/or the signal representing
an angle of incidence.
Each sensor of the plurality of electromagnetic radiation sensors
may include an array of similarly oriented nanoantennas. All the
nanoantennas may be oriented so as to be primarily sensitive to
electromagnetic radiation polarized along the axis of the sensor.
All the nano antennas may be electrically coupled together to
generate the proportional signal for the sensor.
At least one sensor (a "tiltable sensor") of the plurality of
electromagnetic radiation sensors may be tiltable. The star tracker
may also include a motor mechanically coupled to the at least one
tiltable sensor, so as to tilt the at least one sensor from a first
plane to a second plane. The at least one tiltable sensor generates
at least a first portion of the proportional signal, based on a
magnitude of unpolarized electromagnetic radiation detected by the
at least one tiltable sensor while the at least one tiltable sensor
is in the first plane. The at least one tiltable sensor generates a
second portion of the proportional signal, based on a magnitude of
unpolarized electromagnetic radiation detected by the at least one
tiltable sensor while the at least one tiltable sensor is in the
second plane. The ratio detector generates at least a first portion
of the ratio signal based on the first portion of the proportional
signal. The ratio detector generates at least a second portion of
the ratio signal based on the second portion of the proportional
signal.
Yet another embodiment of the present invention provides a computer
program product for determining a direction to a source of
unpolarized electromagnetic radiation. The computer program product
includes a non-transitory computer-readable medium having computer
readable program code stored thereon. When executed by a processor,
the computer readable program code causes the processor to receive
a first signal from a first sensor. The first sensor is exposed to
the unpolarized electromagnetic radiation. The first sensor is
primarily sensitive to electromagnetic radiation polarized along a
first axis. The first sensor is configured to generate the first
signal proportional to a magnitude of the unpolarized
electromagnetic radiation detected by the first sensor. The
computer readable program code is also configured to cause the
processor to receive a second signal from a second sensor. The
second sensor is exposed to the unpolarized electromagnetic
radiation. The second sensor is primarily sensitive to
electromagnetic radiation polarized along a second axis. The second
axis is different than the first axis. The second sensor is
configured to generate the second signal proportional to a
magnitude of the unpolarized electromagnetic radiation detected by
the second sensor. The computer readable program code is configured
to cause the processor to determine a ratio of the first signal to
the second signal. The computer readable program code is configured
to cause the processor to use the ratio to calculate an angle of
incidence of the unpolarized electromagnetic radiation.
The computer readable program code may also cause a processor to
automatically access a database that stores a star catalog and
automatically calculate a location in space based at least in part
on the angle of incidence and information in the star catalog.
The first sensor may be exposed to the unpolarized electromagnetic
radiation by exposing a first array of nanoantennas to the
unpolarized electromagnetic radiation. All nanoantennas of the
first array of nanoantennas may be similarly oriented, so as to be
primarily sensitive to electromagnetic radiation polarized along
the first axis. All the nanoantennas of the first array of
nanoantennas may be electrically coupled together to generate the
first signal. The second sensor may be exposed to the unpolarized
electromagnetic radiation by exposing a second array of
nanoantennas to the unpolarized electromagnetic radiation. All
nanoantennas of the second array of nanoantennas may be similarly
oriented, so as to be primarily sensitive to electromagnetic
radiation polarized along the second axis. All the nanoantennas of
the second array of nanoantennas may be electrically coupled
together to generate the second signal.
The computer readable program code may also cause the processor to
store a value representing the second signal. The computer readable
program code may also cause the processor to tilt the second sensor
and expose the tilted second sensor to the unpolarized
electromagnetic radiation. The computer readable program code may
also cause the processor to generate a third signal proportional to
a magnitude of the unpolarized electromagnetic radiation detected
by the tilted second sensor. Determining the ratio of the first
signal to the second signal and using the ratio to calculate the
angle of incidence of the unpolarized electromagnetic radiation may
include using the first signal, the stored value representing the
second signal and the third signal to calculate the angle of
incidence of the unpolarized electromagnetic radiation.
The computer readable program code may also cause the processor to
compensate for a degree to which the unpolarized electromagnetic
radiation is polarized.
An embodiment of the present invention provides a star tracker for
determining a direction to a source of unpolarized electromagnetic
radiation. The star tracker includes a first electromagnetic
radiation sensor. The first electromagnetic radiation sensor is
configured to generate a first signal proportional to a first
polarization component of unpolarized electromagnetic radiation
impinging on the first electromagnetic radiation sensor. The star
tracker also includes a second electromagnetic radiation sensor.
The second electromagnetic radiation sensor is configured to
generate a second signal proportional to a second polarization
component of unpolarized electromagnetic radiation impinging on the
second electromagnetic radiation sensor. The second polarization
component is oriented differently than the first polarization
component. The star tracker also includes a ratio detector. The
ratio detector receives the first and second signals. The ratio
detector generates a ratio signal that represents a ratio of first
signal to the second signal. The star tracker also includes an
angle of incidence calculator. The angle of incidence calculator
receives the ratio signal and generates therefrom a signal
representing an angle of incidence of the unpolarized
electromagnetic radiation.
Another embodiment of the present invention provides a star tracker
that includes a plurality of electromagnetic radiation sensors.
Each sensor of the plurality of electromagnetic radiation sensors
is configured to generate a respective signal in proportion to
magnitude of a different polarization component of unpolarized
electromagnetic radiation impinging on the sensor. The star tracker
also includes a ratio detector. The ratio detector is configured to
receive the signals generated by the plurality of electromagnetic
radiation sensors. The ratio detector is configured to calculate an
angle of incidence of the unpolarized electromagnetic
radiation.
BRIEF DESCRIPTION OF THE DRAWINGS
The invention will be more fully understood by referring to the
following Detailed Description of Specific Embodiments in
conjunction with the Drawings, of which:
FIG. 1 is a schematic diagram of a star tracker, according to the
prior art.
FIG. 2 is a schematic diagram of a star tracker, according to an
embodiment of the present invention.
FIG. 3 is a schematic diagram of a propagating, linearly polarized,
electromagnetic wave, as known in the prior art.
FIG. 4 is a schematic diagram of a propagating unpolarized
electromagnetic wave, as known in the prior art.
FIG. 5 is a schematic diagram of two polarization-sensitive light
sensors of the star tracker of FIG. 2, according to an embodiment
of the present invention. Incident light, impinging on the two
polarization-sensitive light sensors at an angle of incidence of 0
degrees, is shown.
FIG. 6 is similar to FIG. 5. Incident light, impinging on the two
polarization-sensitive light sensors at several angles of incidence
are shown.
FIG. 7 is a schematic top view of an embodiment of a polarization
sensing element (poxel), which may be used to implement the two
polarization-sensitive light sensors of FIGS. 2, 5 and 6, according
to an embodiment of the present invention.
FIG. 8 is a schematic top view of another embodiment of a
polarization sensing element (poxel), according to an embodiment of
the present invention.
FIG. 9 is a schematic perspective view of a baffle around one
element of a poxel, according to an embodiment of the present
invention.
FIG. 10 is a schematic diagram similar to FIGS. 5 and 6, except the
incident light vector lies in a plane that is not aligned with
either of the two polarization-sensitive light sensors.
FIG. 11 is a schematic top view of a six-axis
polarization-sensitive light sensor, according to an embodiment of
the present invention.
FIG. 12 is a schematic top view of an eight-axis
polarization-sensitive light sensor, according to an embodiment of
the present invention.
FIG. 13 is a perspective schematic view of a non-coplanar five-axis
polarization-sensitive light sensor, according to an embodiment of
the present invention.
FIG. 14 is a perspective schematic view of a non-coplanar five-axis
polarization-sensitive light sensor with articulated segments,
according to an embodiment of the present invention.
FIG. 15 is a perspective schematic view of a tiltable single
segment polarization-sensitive light sensor, according to an
embodiment of the present invention.
FIG. 16 is a schematic diagram of a star tracker, according to
another embodiment of the present invention. The embodiment
illustrated in FIG. 16 is similar to the embodiment of FIG. 2,
however the embodiment of FIG. 16 includes a light-gathering
lens.
FIG. 17 is a perspective schematic view of a semiconductor nanowire
antenna, which may be used to implement each element of the poxel
of FIGS. 7 and 8, according to an embodiment of the present
invention.
FIG. 18 is a schematic flowchart illustrating a method for
determining a direction to a source of unpolarized electromagnetic
radiation, such as light from a star, according to an embodiment of
the present invention.
FIG. 19 is a schematic flowchart illustrating optional operations
for the method of FIG. 18.
FIG. 20 is a perspective schematic view of a non-coplanar
three-poxel polarization-sensitive light sensor, according to
another embodiment of the present invention.
FIG. 21 is a schematic diagram of two hypothetical sets of
coordinate axes, one set being rotated an arbitrary amount with
respect to the other.
FIG. 22 is a schematic diagram of a hypothetical Poynting vector
and a set of coordinate axes.
DETAILED DESCRIPTION OF SPECIFIC EMBODIMENTS
In accordance with embodiments of the present invention, methods
and apparatus are disclosed for determining a location or
orientation of an object, such as a vehicle, by observing light
from one or more stars or other relatively bright navigational
marks, without imaging optics. Thus, these embodiments can be
smaller and lighter than conventional star trackers. These
embodiments do not require power-hungry pixelated imaging sensors
and associated pixel readout electronics. Some embodiments have
vertical profiles of essentially just their optical sensors.
Embodiments of the present invention measure angles of incidence of
light, relative to optical sensors, by comparing signals from two
or more differently polarized optical sensors. The embodiments do
not, however, require the light to be polarized.
FIG. 1 is a schematic diagram of a star tracker 100, according to
the prior art. Light from a star 102 is focused by a lens 104 onto
a pixelated image sensor 106. In some cases, the focused image
occupies a single pixel, as indicated at 108. In other cases, the
focused image occupies several adjacent pixels. A camera controller
110 reads data from the pixels of the image sensor 106 to generate
digital image data. Collectively, the lens 104, the images sensor
106 and the camera controller 110 form a digital camera 112.
An image processor 113 then analyzes the image data to determine a
centroid location of the star image on the image sensor 106. In
some cases, more than one star is imaged, in which case the image
processor 113 determines centroid locations for each of the star
images. From the location(s) of the centroid(s), typically relative
to the center of the image, the image processor 113 calculates
angles to each imaged star.
A star catalog 116 stores information about selected navigational
stars, such as information about their locations in the sky or
information for calculating their sky locations based on time and
date. The information in the star catalog 116 is sufficient to
enable a navigation calculator 114 to calculate a location and/or
attitude of the vehicle in space, given the relative angle(s). The
prior art start tracker 100 is, therefore, sensitive to distortion
of the lens 104 and to misalignment of the lens 104 with the image
sensor 106. Such misalignment may occur during manufacture or
result from thermal expansion and contraction in space or from
vibration or other forces during launch.
FIG. 2 is a schematic diagram of a star tracker 200, according to
an embodiment of the present invention. Light from a star 202
illuminates two polarization-sensitive light sensors 204 and 206.
The light from the star 202 may be within any portion of the
electromagnetic spectrum that can be reliably detected by the
polarization-sensitive light sensors 204 and 206, not necessarily
within the visible or invisible light portions of the spectrum
(about 50 nm to about 500 .mu.m). Collectively, the two
polarization-sensitive light sensors 204 and 206 are referred to
herein as a "polarization sensing element" (poxel) 208. Each
polarization-sensitive light sensor 204 and 206 is sensitive to
light polarized along a different axis, as indicated by arrows 210
and 212, respectively. In some embodiments, the two axes 210 and
212 are mutually perpendicular. Note, however, that each
polarization-sensitive light sensor 204 and 206 can, but need not,
be pixelated.
Star light is essentially unpolarized or only very slightly
polarized. Although integrated thermal radiation of stars is not
usually appreciably polarized at source, scattering by interstellar
dust can impose polarization on starlight over long distances. Net
polarization at the source can occur if the photosphere itself is
asymmetric, due to limb polarization. Plane polarization of
starlight generated at the star itself is observed for Ap stars
(peculiar A type stars). Star light observed near earth is
polarized to a maximum degree of about 2%. Unless context indicates
otherwise, as used herein, the term unpolarized light means light
with a maximum degree of polarization of about 2%.
As described herein, a relative amount by which each of the
polarization-sensitive light sensors 204 and 206 is stimulated
depends largely on an angle of incidence of the light from the star
202, even with completely unpolarized light. That is, the angle of
incidence determines a ratio, according to which one of the
polarization-sensitive light sensors 204 is stimulated, relative to
the other polarization-sensitive light sensor 206. Embodiments of
the present invention do not, therefore, rely on receiving
polarized light.
Each polarization-sensitive light sensor 204 and 206 generates a
respective signal 214 and 216, such as a voltage, in proportion to
an amount of light detected by the polarization-sensitive light
sensor. A ratio detector 218 determines a ratio of the signals 214
and 216. This ratio correlates to the angle of incidence, as
discussed herein. An angle calculator 219 calculates an angle of
incidence of the light from the star, based on the ratio of the
signals 214 and 216. A bearing angle to the star 202, relative to
the polarization-sensitive light sensor 204 and 206, is equal to
the angle of incidence. The bearing angle calculator 219 provides
the bearing angle to a navigation calculator 220.
The navigation calculator 220 uses the bearing angle information
and a star catalog 222, largely as in a conventional star tracker,
to calculate a location and/or attitude of the star tracker and/or
its vehicle. The ratio detector 218 may be implemented with a
suitable analog comparator, and the bearing angle calculator 291
may be implemented with a suitable processor executing instructions
stored in a memory, such as a read-only memory (ROM).
Alternatively, the signals 214 and 216 may be digitized by suitable
analog-to-digital converters, and digitized data may be analyzed by
the bearing angle calculator 219. The navigation calculator 220 may
be implemented by a processor executing instructions stored in a
memory. One processor may implement both the bearing angle
calculator 219 and the navigation calculator 220, or separate
processors may be used. The star catalog 222 may be stored in a
non-volatile memory, such as a read-only memory (ROM), disposed
proximate the navigation calculator 220.
In some embodiments, a single integrated circuit includes both the
star catalog 222 and the navigation calculator 220. In some
embodiments, the star catalog 222 is stored remote from the
navigation calculator 220, such as in a server on earth, while the
navigation calculator 220 is disposed in a vehicle in space. The
processor(s) execute instructions in order to perform algorithms,
such as to calculate a bearing angle from the ratio of signals 214
and 216, as described herein.
As noted, embodiments of the present invention do not rely on
receiving polarized light. However, FIGS. 3 and 4 provide
background information about polarization, polarized light and
unpolarized light, which may be useful in understanding embodiments
of the invention. Electromagnetic radiation, referred to herein as
"light," behaves as waves propagating through space, and also as
photon particles traveling through space. As an electromagnetic
wave, electromagnetic radiation has both electric field and
magnetic field components, which oscillate in fixed phase
relationship to each other, and spatially perpendicular to each
other and perpendicular to the direction of propagation.
FIG. 3 schematically illustrates a hypothetical electric field
component 300 of a linearly polarized electromagnetic wave
propagating along an axis 302 in a direction indicated by arrow
304. The electric field component 300 oscillates sinusoidally
within a plane 306 that includes the propagation axis 302. As the
wave 300 propagates, its electric field can be conceptualized as a
set of arrows indicating direction and intensity (vectors) of the
electric field, exemplified by arrows 308, within the plane 306.
The wave 300 is said to be polarized within the plane 306 or along
a line 310 within the plane 306 and perpendicular to the axis of
propagation 302.
For simplicity, the magnetic field component is omitted from FIG.
3. However, the magnetic field component also propagates along the
axis 302. The magnetic field component oscillates in a plane (not
shown) that is perpendicular to the electric field plane 306.
As noted, the electromagnetic radiation depicted in FIG. 3 is
linearly polarized. Its electric field component is confined to a
plane 306, and its magnetic field component is confined to a
perpendicular plane (not shown).
Most common sources of visible light, including thermal (black
body) radiation, such as star light, and fluorescence (but not
lasers), produce light described as incoherent. In this case,
radiation is produced, i.e., photons are emitted, independently by
a large number of atoms or molecules whose emissions are
uncorrelated with each other and generally of random polarizations.
Thus, essentially, each photon produced is randomly polarized. In
this case, the light is said to be unpolarized. This term is
somewhat inexact, since at any instant of time, at one location,
there is a definite direction to the electric and magnetic fields.
However, the term unpolarized implies that the polarization changes
so quickly in time that it will not be measured or it is irrelevant
to the outcome of an experiment. Over time, a receiver of
unpolarized light receives all possible polarizations.
FIG. 4 schematically illustrates hypothetical electric field
vectors, exemplified by vectors 400, of an unpolarized
electromagnetic wave at a point along an axis 402 of propagation.
In contrast with the linear polarized light of FIG. 3, over time,
the electric field vectors 400 aim in all directions radially away
from the propagation axis 402. The electric field vectors 400 all
lay within a plane 404 perpendicular to the axis of propagation
402. The magnetic field components are omitted for clarity.
As noted with respect to FIG. 2, unpolarized light from the star
202 impinges on two polarization-sensitive light sensors 204 and
206. FIG. 5 is a schematic diagram of the two
polarization-sensitive light sensors 204 and 206, shown separated
for clarity. In FIG. 5, the propagation axis of the light is
assumed to be normal (perpendicular) to the polarization-sensitive
light sensors 204 and 206, i.e., the angle of incidence is 0
degrees. Light radiation from the star is represented by a
propagation vector K.sub.1. The light from the star is unpolarized,
as indicated by electric field vectors aimed in all possible
directions within a plane 500 perpendicular to the vector K.sub.1.
The electric field vectors are exemplified by vectors 502, 504, 506
and 508. The magnetic field components are omitted for clarity.
Light sensor 204 is sensitive to light polarized along its axis
210, whereas light sensor 206 is sensitive to light polarized along
a different axis 212. Thus, light sensor 204 is stimulated
primarily by photons whose polarizations correspond to electric
field vectors oriented parallel to its axis 210, such as electric
field vectors 504 and 508, shown in bold in the upper portion of
FIG. 5. To a lesser extent, the light sensor 204 may be stimulated
by photons of other polarizations.
Similarly, light sensor 206 is stimulated primarily by photons
whose polarizations correspond to electric field vectors oriented
parallel to its axis 212, such as electric field vectors 502 and
506, shown in bold in the lower portion of FIG. 5. To a lesser
extent, the light sensor 206 may be stimulated by photons of other
polarizations.
As noted, each polarization-sensitive light sensor 204 and 206
generates a respective signal S.sub.1 and S.sub.2, such as a
voltage, in proportion to the amount of light detected by the light
sensor. Because the star light is unpolarized (each photon is
randomly polarized), the amount of radiation polarized along the
axis 210 is equal to the amount of radiation polarized along the
axis 212. The vector K.sub.1 is normal to the two light sensors 204
and 206. Thus, each light sensor 204 and 206 is equally stimulated.
S.sub.1=S.sub.2, thus the ratio S.sub.1/S.sub.2=1. A ratio of 1
indicates the angle of incidence is 0 degrees.
FIG. 6 is similar to FIG. 5; however two additional vectors K.sub.2
and K.sub.3 are shown. Vector K.sub.2 represents light from a star
impinging on the two polarization-sensitive light sensors 204 and
206 at an incident angle .theta..sub.2, and vector K.sub.3
represents light from a star impinging on the two
polarization-sensitive light sensors 204 and 206 at an incident
angle .theta..sub.3. The vectors K.sub.1, K.sub.2 and K.sub.3 lie
in a plane 600 that is perpendicular to the polarization-sensitive
light sensors 204 and 206, perpendicular to the polarization axis
210 of polarization-sensitive light sensor 204 and parallel to the
polarization axis 212 of polarization-sensitive light sensor
206.
Electric field vectors 504 and 508 are shown in the upper portion
of FIG. 6. Recall that electric field vectors 504 and 508 are
parallel to the axis 210, along which the polarization-sensitive
light sensor 204 is sensitive. Electric field vectors 502 and 506
are shown in the lower portion of the figure. Recall that electric
field vectors 502 and 506 are parallel to the axis 212, along which
the polarization-sensitive light sensor 206 is sensitive. The other
electric field vectors are omitted for clarity, although they may
stimulate the polarization-sensitive light sensors 204 and 206 to
extents, depending on their polarization angles, relative to the
polarization axes 210 and 212.
Regardless of the angle of incidence .theta., electric field
vectors 504 and 508 remain perpendicular to the plane 600 and
parallel to the axis 210 of the polarization-sensitive light sensor
204. Therefore, the amount by which the polarization-sensitive
light sensor 204 is stimulated is largely independent of the angle
of incidence .theta..
However, the electric field vectors 502 and 506 are in the plane
600. These electric field vectors 502 and 506 are parallel to the
axis 212 of the polarization-sensitive light sensor 206 only when
the angle of incidence .theta. is zero. As the angle of incidence
.theta. increases from 0 to 90 degrees, the electric field vectors
502 and 506 become progressively less parallel, and progressively
more perpendicular, to the axis 212 of the polarization-sensitive
light sensor 206. Consequently, the amount by which the
polarization-sensitive light sensor 206 is stimulated is highly
dependent on the angle of incidence .theta..
Another way of expressing the concepts shown in FIG. 6 involves
noting that the polarization state of each photon of incoming star
light is perpendicular to the light's propagation vector K.sub.n,
even if the light is unpolarized. The light may, in general, be
represented by randomly polarized light, where the Stokes vector
can be decomposed into two orthogonal polarization components. The
two orthogonal polarization components define a plane that is
perpendicular to the path of propagation of the star light. These
orthogonal polarization components are detected by the
polarization-sensitive light sensors 204 and 206. Each of the
polarization-sensitive light sensors 204 and 206 does not
necessarily detect one of the two orthogonal polarization
components. Instead, the ratio of the signals from the
polarization-sensitive light sensors 204 and 206, and in some cases
from an additional one or more polarization-sensitive light
sensors, is used to resolve the two orthogonal polarization
components. The path of propagation of the star light is then
calculated from the two polarization components, based on the
knowledge that the path is perpendicular to both of the decomposed
polarization components.
FIG. 7 is a schematic top view of an embodiment of a polarization
sensing element (poxel) 700, according to an embodiment of the
present invention. The poxel 700 is shown as being rectangular;
however, other shapes can be used. The poxel 700 is preferably
fabricated using semiconductor wafer fabrication techniques. The
poxel 700 includes a sub-millimeter thin substrate with nanoscale
elements, exemplified by elements 702, 704, 706 and 708, on its
surface. The elements 702-708 directly sense polarization
components of incoming light. In some embodiments, the elements
702-708 are nanoantennas. These may be optical nanoantennas,
rectennas, nanophotonic phased arrays, nanomaterials (such as
metal-on-graphene), plasmonic antennas, or the like. These elements
may be patterned directly on the surface of the poxel using
conventional semiconductor fabrication techniques, such as
electron-beam (e-beam) lithography or deep-ultraviolet (deep-UV)
photolithography. Nanometallic, such as plasmonic, structures may
be used to concentrate light into deep-subwavelength volumes,
facilitating sensing electromagnetic radiation having visible, near
visible or invisible wavelengths, as discussed by Jon A. Schuller,
et al., in Plasmonics for extreme light concentration and
manipulation, pp. 193-204, Nature Materials, Vol. 9, March 2010,
the entire contents of which are hereby incorporated by
reference.
The poxel 700 may include any number of elements 702-708. In most
embodiments, half the elements 702-708 are oriented along the axis
210 (FIG. 6) of one polarization-sensitive light sensor 204, and
the other half of the elements 702-708 are oriented along the axis
212 of the other polarization-sensitive light sensor 206. For
example, as illustrated in FIG. 7, elements 702 and 706 may be
oriented parallel to a Y axis (as is axis 210), whereas elements
704 and 708 may be oriented parallel to an X axis (as is axis 212).
In the embodiment of FIG. 7, the element orientations alternate
along rows and columns. However, other arrangements of orientations
may be used. For example, as shown schematically in FIG. 8, a poxel
800 may have like-oriented elements grouped together.
Returning to FIG. 7, the number of elements 702-704 may be selected
based on a desired overall size and/or shape of the poxel 700 and
the size of each element, which may depend on the wavelength of the
radiation to be detected. Some embodiments may include about 1,000
elements of each orientation, for example.
All like-oriented elements 702-708 may be electrically connected
together, preferably within the substrate, thus voltages generated
by all the like-oriented elements add together, and their signals
are made available on signal lines, such as signal lines S.sub.A
and S.sub.B. The signal lines S.sub.A and S.sub.B correspond to the
signal lines S.sub.3 and S.sub.4 in FIG. 6. To limit physical
distortion of the poxel, the substrate material and construction
should be selected to have a low coefficient of thermal expansion,
because most practical materials do not expand isometrically in
response to changes in temperature. Furthermore, in many
applications, such as space-based applications, the poxel may be
heated unevenly.
FIG. 17 is a perspective schematic view of a
metal-semiconductor-metal germanium photodetector/semiconductor
nanowire antenna 1700. Each element 702-708 of the poxel 700 (FIG.
7) may be implemented as such a nanowire antenna 1700. As noted by
Linyou Cao, et al., in Resonant Germanium Nanoantenna
Photodetectors, pp. 1229-1233, Nano Letters, 2010 (hereinafter
"Cao"), the contents of which are hereby incorporated by reference,
a sufficiently large nanowire 1702 can be thought of as a
cylindrical cavity antenna that traps incident light 1704 in
circulating orbits by multiple total internal reflections from the
periphery of the nanowire 1702, as indicated by arrows 1706. FIG.
17 is based on an illustration from Cao.
The nanowire antenna 1700 may be fabricated by intrinsically
growing a germanium (Ge) nanowire 1702 using a chemical vapor
deposition process, and electrical contacts 1708 and 1710, for
example 2 nm of Ti/400 nm of Al and 5 nm of Cr/400 nm of Pt), may
be defined at the ends of the nanowire 1702 with standard e-beam
lithography, metal deposition and lift-off techniques. The
electrode metals may be chosen to form an asymmetric
metal-semiconductor-metal detector, with one Schottky contact 1708
and one Ohmic contact 1710.
The nanowire antenna 1700 is both wavelength and polarity
selective, based on the size and orientation of the nanowire 1702.
The nanowire 1702 may be designed to be resonant at a desired
wavelength, such as at a peak in the electromagnetic spectrum of a
star of interest. A plurality of nanowires of various sizes, and
therefore resonant at a variety of wavelengths, may be included in
a single poxel 700 (FIG. 7) to provide multiple wavelength or
broadband sensitivity, or all the nanowires may be of identical
size.
Returning to FIG. 6, if S.sub.4 represents magnitude of the signal
from the polarization-sensitive light sensor 204, and S.sub.3
represents magnitude of the signal from the polarization-sensitive
light sensor 206, S.sub.3=S.sub.4 cos .theta.. The ratio of the
magnitudes of the signals from the two polarization-sensitive light
sensors 204 and 206 is S.sub.3/S.sub.4=S.sub.4 cos
.theta./S.sub.4=cos .theta.. Thus, the angle of incidence .theta.
may be determined from the ratio S.sub.3/S.sub.4. As noted, all the
vectors K.sub.n in FIGS. 5 and 6 lie in the plane 600.
FIG. 18 is a schematic flowchart illustrating a method for
determining a direction to a source of unpolarized electromagnetic
radiation, such as light from a star. At 1800, a first sensor is
exposed to the unpolarized light from the source of unpolarized
electromagnetic radiation. The first sensor is sensitive to
electromagnetic radiation polarized along a first axis. The sensor
generates a first signal proportional to the magnitude and
direction of the unpolarized electromagnetic radiation detected by
the first sensor. The first sensor may include a first array of
nanoantennas, all similarly oriented, so as to be primarily
sensitive to electromagnetic (EM) radiation polarized along the
first axis. All the nanoantennas of the first array of nanoantennas
may be electrically coupled together.
At 1802, a second sensor is exposed to the unpolarized light. The
second sensor is sensitive to electromagnetic radiation polarized
along a second axis, different than the first axis. The sensor
generates a second signal proportional to the magnitude and
direction of the unpolarized electromagnetic radiation detected by
the second sensor. The second sensor may include a second array of
nanoantennas, all similarly oriented, so as to be primarily
sensitive to EM radiation polarized along the second axis. All the
nanoantennas of the second array of nanoantennas may be
electrically coupled together.
At 1804, a ratio of the first signal to the second signal is
determined. At 1806, a database storing a star catalog is accessed.
At 1808, the ratio is used to calculate an angle of incidence. At
1810, the angle of incidence and information, such as angles of
incidence to various stars, in the star catalog is used to
calculate an orientation in space. An optional operation 1812 is
described below.
Returning to FIG. 6, it should be noted that a given ratio of
S.sub.3/S.sub.4 can represent two different vectors K.sub.n, as
illustrated by vector K'.sub.2, which is symmetric with vector
K.sub.2. If a star of interest is known to be within a
quarter-sphere field of view centered on the polarization-sensitive
light sensors 204 and 206, this ambiguity can be resolved by
ignoring the symmetric vector that falls outside the quarter
sphere.
Optionally or alternatively, some or all the elements of the poxel
may have baffles to block portions of what would otherwise be their
fields of view, as shown schematically in FIG. 9. FIG. 9 shows one
baffle. The baffles should be largely or completely opaque to EM
radiation at wavelengths of interest. Such baffles may be used to
block a portion of the field of view, so as to prevent the element
being illuminated by light from an undesired source, such as the
sun or a star not used for navigation. For example, the baffles may
be constructed so as to limit a poxel's field of view to a single
star.
FIG. 9 shows one element 900 of a poxel. Walls 902, 904, 906 and
908 extend upward from the substrate 910 and limit the field of
view of the element 900. Each element of a poxel, or each element
of a polarization-sensitive light sensor, may have a similar set of
walls forming a respective baffle. All the walls 902-908 in FIG. 9
are shown to be vertical, relative to the substrate 910, and of
equal height. However, different walls may be of different heights
and/or different angles, relative to the substrate 910, depending
on a desired field of view for the element 900.
Similarly, all the elements need not have identical fields of view.
For example, all elements having a first orientation may all have a
first field of view, whereas all elements having a second,
different, orientation may have a second, different, field of view.
The walls 902-908 may be fabricated by conventional semiconductor
fabrication techniques. Although a square baffle, comprising four
walls 902-908, is shown, other numbers of walls and other shape
baffles may be used. Each wall 902-908 may also be part of a baffle
for an adjacent element (not shown). Although only one element is
disposed within the baffle shown in FIG. 9, other numbers of
similarly- or differently-oriented elements may be disposed within
each baffle.
As noted with respect to FIG. 6, using two polarization-sensitive
light sensors 204 and 206, an angle of incidence .theta. may be
determined, with a possibility of one ambiguity, if the incident
light lies within a plane 600 aligned with one of the two axes 210
or 212 of the polarization-sensitive light sensors 204 and 206. In
some cases, these constrains are acceptable. However, in other
cases, the incident light cannot be assumed to lie within the plane
600. For example, as schematically illustrated in FIG. 10, the
incident light vector K.sub.4 may lie in a plane 1000 that is
perpendicular to the polarization-sensitive light sensor 204 or
206, but that is rotated by an angle .phi. about a Z axis. In such
cases, the ratio of signals from the two polarization-sensitive
light sensors 204 and 206 yield several ambiguities. If these
ambiguities are acceptable, for example if the possible directions
from which the impinging light originates are constrained
sufficiently to avoid the ambiguities, two polarization-sensitive
light sensors 204 and 206 may be sufficient.
In other cases, additional polarization-sensitive light sensors,
aligned differently than the polarization-sensitive light sensors
204 and 206, may be included to remove the ambiguities. For
example, FIG. 11 is a schematic top view of a six-axis
polarization-sensitive light sensor 1100, according to an
embodiment of the present invention. The six-axis
polarization-sensitive light sensor 1100 contains six segments
1102, 1104, 1106, 1108, 1110 and 1112. Each segment 1102-1112 is
sensitive to light polarized along its respective axis, indicated
by arrows 1114, 1116, 1118, 1120, 1122 and 1124, respectively.
FIG. 12 is a schematic top view of an eight-axis
polarization-sensitive light sensor 1200, according to an
embodiment of the present invention. The eight-axis
polarization-sensitive light sensor 1200 contains sixteen segments,
exemplified by segments 1202, 1204 and 1206. Each segment 1202-1206
is sensitive to light polarized along its respective axis,
indicated by arrows within the segments 1202-1206.
The embodiments described with respect to FIGS. 11 and 12 are
planar. Optionally or alternatively, non-coplanar
polarization-sensitive light sensors may be used to remove the
ambiguities. FIG. 13 is a perspective schematic view of a
non-coplanar five-axis polarization-sensitive light sensor 1300,
according to an embodiment of the present invention. The sensor
1300 includes five non-coplanar segments 1302, 1304, 1306, 1308 and
1310. Each segment 1302-1304 includes two sets of differently
oriented elements. The segments 1302-1310 may be fabricated
separately or together on a common substrate.
FIG. 20 is a perspective schematic view of a non-coplanar
three-poxel polarization-sensitive light sensor 2000, according to
an embodiment of the present invention. Each surface (segment)
2002, 2004 and 2006 contains two sets of differently oriented
elements. The elements are not shown in FIG. 20.
Optionally or alternatively, one or more segments of a
polarization-sensitive light sensor may be hinged, so the segment's
orientation may be changed, relative to another segment of the
polarization-sensitive light sensor, as schematically illustrated
in FIG. 14. In such an embodiment, the hinged segments are referred
to herein as being articulated. The five-axis
polarization-sensitive light sensor 1400 is similar to the
five-axis polarization-sensitive light sensor 1300 described with
respect to FIG. 13. However, one or more of the segments 1404,
1406, 1408 and/or 1410 are mounted via hinges, three of which are
visible at 1412, 1414 and 1416. The hinges 1412-1416 enable their
respective segments 1404-1410 to pivot, as indicated by curved
arrows, relative to each other and to segment 1402.
The segments 1404-1410 may be driven by suitable motors,
represented by motor 1418, such as a piezoelectric motor,
ultrasonic linear motor, microelectromechanical (MEMS) motor or
another suitable drive system. Tilting one or more of the segments
1404-1410 enable the ratio detector 218 (FIG. 2) or the bearing
angle calculator 219 to resolve one or more ambiguities. The
motor(s) may be driven by the ratio detector 218 (FIG. 2), the
angle calculator 219 and/or the navigation calculator 220 (FIG.
2).
Some embodiments, such as the embodiment 1500 schematically
illustrated in FIG. 15, have only one segment that can be oriented
by a suitable motor to any of several tilts by a suitable motor
1502. In either case, the ratio detector 218 (FIG. 2) and/or the
angle calculator 219 may read data from the polarization-sensitive
light sensors and then cause one or more segments to tilt, and then
read additional data from the polarization-sensitive light sensor.
In other words, two sets of data may be read from one or more of
the polarization-sensitive light sensors, one data set before, and
the other data set after, the sensor is tilted. A suitable memory
may be used to store the first data set while the second data set
is being acquired. Similarly, data may be read before the sensor is
tilted and the data may be stored, and then data may be read after
each tilt of a series of tilts. Although the embodiment illustrated
in FIG. 15 tilts about one axis 1504, some other embodiments can
tilt the sensor 1506 about two axes using one or two appropriate
motors 1502.
FIG. 19 is a schematic flowchart illustrating optional operations
for the method of FIG. 18, in relation to tilting a segment of a
poxel. At 1900, a value representing the second signal is stored.
At 1902, the second sensor is tilted. At 1904, the tilted second
sensor is exposed to the EM radiation. At 1906, a third signal is
generated. The third signal is proportional to a magnitude of the
unpolarized EM radiation detected by the tilted second sensor.
Determining the ratio of the first signal to the second signal 1804
(FIG. 18) and using the ratio to calculate the angle of incidence
of the unpolarized electromagnetic radiation 1808 includes using
the first signal, the stored value representing the second signal
and the third signal to calculate the angle of incidence of the
unpolarized electromagnetic radiation, as indicated at 1908 (FIG.
19).
As noted, prior art star trackers include pixelated image sensors.
The sensitivities of these image sensors depend on wavelength of
incident light. However, polarization of the incident light does
not depend on wavelength. Therefore, the polarization-sensitive
light sensors described herein should provide sensitivity and
signal-to-noise characteristics at least as good as conventional
image sensor-based star trackers.
Optionally, a lens 1600 may be disposed in front of the
polarization-sensitive light sensors 204 and 206 to increase the
light capture area (aperture), as schematically illustrated in FIG.
16. The lens 1600 may be larger than the polarization-sensitive
light sensors 204 and 206 to provide a larger EM capture aperture.
The lens 1600 need not be focused on the polarization-sensitive
light sensors 204 and 206, and its alignment is not critical.
In some embodiments, the poxel elements include materials, such as
metal-on-graphene, that are inherently more resistant to
high-energy radiation than silicon-based devices, such as
conventional image sensors. Resistance to high-energy radiation is
important in space-based applications, because in these
applications, vehicles are routinely subjected to high-energy
radiation, such as heavy ions, neutrons and protons.
Light is said to be partially polarized when there is more power in
one polarization mode than another. At any particular wavelength,
partially polarized light can be statistically described as the
superposition of a completely unpolarized component, and a
completely polarized one. One may then describe the light in terms
of the degree of polarization, and the parameters of the polarized
component.
As noted, Jinkui Chu's polarization-based navigation system
requires polarized light. Chu's system includes six light sensing
photodiodes arranged in pairs. A polarizing filter is disposed in
front of each photodiode. The polarizing filters of each pair of
photodiodes are orthogonally oriented, relative to each other. The
three pairs of polarizing filters are oriented at 0, 60 and 120
degrees, with respect to each other. A blue filter is disposed in
front of the six polarizing filters. The entire collection of
photodiodes, polarizing filters and blue filter is aimed straight
up at the sky, a point Chu refers to as the "zenith," although
Chu's device depends on light scattered by earth's atmosphere, not
on stars in the celestial sphere.
Chu discloses a system of multiple equations in multiple unknowns,
which is solved to ascertain an angle between the 0 degree
orientation of the navigation sensor and the solar meridian. These
equations include equation (1): S.sub.ij(.phi.)=KI(1+d
cos(2.phi.-2.phi..sub.max)), i=1,2,3; j=0,1 (1) where d is the
degree of polarization, .phi. is the current orientation with
respect to the solar meridian, K is a constant, I is total
intensity and .phi..sub.max is a value that maximizes S(.phi.).
Index i appears to be stepped through the three photodiode pairs,
and index j appears to be stepped through the photodiodes of a
given pair of photodiodes.
Clearly, from equation (1), if the degree of polarization d is
zero, i.e., if unpolarized light impinges on Chu's device, the
equations produce no useful result. Star light is unpolarized, or
at most insufficiently polarized for Chu's device to produce a
useful result. Structurally, if unpolarized light impinges on Chu's
device, equal amounts of light are transmitted by the polarization
filters to the photodiodes, regardless of the angle of incidence.
Therefore, equal amounts of light impinge on each photodiode,
regardless of the angle of incidence. Signals from the photodiodes
do not, therefore, contain any information about the angle of
incidence. In fact, Chu does not describe his device as determining
an angle of incidence. Instead, Chu describes his device as
determining an angle between the 0 degree orientation of the
navigation sensor and the solar meridian. Consequently, Chu's
device is incapable of determining the angle of incidence of any
light, and the device is incapable of determining any angle with
respect to unpolarized light.
In contrast, embodiments of the present invention work with
unpolarized light. If the light impinging on the
polarization-sensitive light sensors is polarized or partially
polarized, the ratio detector 218 (FIG. 2) and/or the angle
calculator 219 could compensate for the degree of polarization,
because operation of the disclosed embodiments assumes the light is
completely unpolarized. It is assumed that light impinging on each
polarization-sensitive light sensor contains equal numbers of
photons of every possible polarization. If this is not true, the
signal from the polarization-sensitive light sensor whose
orientation is closest to the (even slightly) polarized light
should be reduced by an appropriate amount to compensate for the
polarization of the light. Optionally or alternatively, the
calculated ratio may be adjusted, or the calculated angle of
incidence may be adjusted or the location in space may be adjusted
to compensate for the degree of polarization. FIG. 18 includes an
optional operation 1812 for compensating for the degree of
polarization. The degree of polarization of expected light sources
may be stored in the star catalog 222 (FIG. 2). Thus, embodiments
of the present invention are structurally different than the Chu
device, and methods of the present invention operate differently
than Chu's device.
General Case of Three Poxels with Differing Orientations
This section contain mathematical explanations of processing of
signals from three differently-oriented poxels, i.e., each poxel is
oriented differently than the other two poxels, according to
embodiments of the present invention. The three-poxel
polarization-sensitive light sensor 2000 of FIG. 20 may be used to
generate such signals. This section contains equations and text
describing mathematical processing of the signals to calculate a
direction, from the poxels, to a star or other light source.
Equations (5) to (16) and their accompanying text assume irradiance
of the star or other light source is known. For example, if one or
more stars are to be used for navigation, published data about
their irradiances may be stored in the star catalog 222 (FIG. 2).
Equations (17) to (31) and their accompanying text assume the
irradiance is not known a priori.
Consider a case of three poxels, whose sensitive elements lay along
the x and y axes of their respective coordinate systems. The three
poxels' orientations are related through rotation angles .alpha.,
.beta. and .gamma., which are described with respect to two sets of
coordinate axes shown in FIG. 21. An initial coordinate or axis is
denoted without a prime, for example x. A first rotated coordinate
or axis is denoted by a single prime, for example x'. A second
rotated coordinate or axis is denoted by a double prime, for
example x''. A third rotated coordinate or axis is denoted by a
capital letter, for example X. The rotation angles .alpha., .beta.
and .gamma. are defined as follows:
.alpha.=angle about z
.beta.=angle between z and {circumflex over (z)}' about {circumflex
over (x)}'
.gamma.=angle about {circumflex over (z)}''
The rotation matrix from x, y, z to X, Y, Z is:
.times..times..times..times..times..times..times..times..times..times..t-
imes..times..times..times..times..times. ##EQU00001## where 1, 2
and 3 represent angles .alpha., .beta. and .gamma., and S and C
represent sine and cosine. So, for example, S.sub.2=sin(.beta.). In
general:
.ident. ##EQU00002##
We take the incident plane wave as unpolarized and represent it as
a vector S, which is the negative time-averaged Poynting vector
with units of watts/meter.sup.2. See FIG. 22. We wish to find all
three components of S by measuring only voltages on the sensitive
poxel elements lying parallel to x and y in their respective
coordinate frames. The poxels are calibrated such that incident
unpolarized light along {circumflex over (z)} yields voltages
V.sub.x and V.sub.y, where: V.sub.x=AS.sub.z and V.sub.y=AS.sub.z
(4) where A is a calibration constant with units of
voltsmeter.sup.2watts.sup.-1. In general, for S not parallel to the
z axis, we have: V.sub.x=|S.times.{circumflex over (x)}|= {square
root over (S.sub.y.sup.2+S.sub.z.sup.2)}= {square root over
(S-S.sub.x.sup.2)} (5) and similarly for V.sub.y: V.sub.y= {square
root over (S.sub.x.sup.2+S.sub.z.sup.2)}= {square root over
(S-S.sub.y.sup.2)} (6) V.sub.x and V.sub.y are the voltages for the
poxel elements aligned with the x and y axes. S is the negative
time-averaged Poynting vector. {circumflex over (x)} denotes a unit
vector pointing along the positive x direction. The | | is the
magnitude of a vector. A vector cross product is denoted by a cross
(".times.") symbol, as in S.times.{circumflex over (x)}.
Since the magnitude of S does not change in any coordinate system,
we have: S=S'=S'' (7)
In general we have:
##EQU00003## for all coordinate systems, V.sub.i being the voltage
along axis z', and S.sub.i being the component of S along axis z'.
We restrict ourselves to: S.sub.z,S.sub.z' and S.sub.z''>0 (9)
i.e., incident light is above the plane of a poxel.
|S|=S=S.sub.x.sup.2+S.sub.y.sup.2+S.sub.z.sup.2+S.sub.x'.sup.2+S.sub.y'.s-
up.2+S.sub.z'.sup.2=S.sub.x''.sup.2+S.sub.y''.sup.2+S.sub.z''.sup.2
(10)
What is known is all poxel voltages V.sub.x, V.sub.y, V.sub.x',
V.sub.y', V.sub.x'' and V.sub.y'' and all rotation angles .alpha.,
.beta. and .gamma.. What is wanted is the time-averaged Poynting
vector, S.
Combining equations (8) and (10) and assuming S is known, i.e., the
star irradiance, we have:
.times..times..times..times.'''.times..times..times..times.'.times..times-
..times..times..times..times.'' ##EQU00004##
So, now we know S.sub.z, S.sub.z' and S.sub.z''.
Let the rotation matrix from the x, y and z to x', y' and z' be and
for x'', y'' and z''. So, in general:
S'=SS.sub.z'=R.sub.31S.sub.x+R.sub.33S.sub.y+R.sub.33S.sub.z (14)
We choose our rotation angles for poxel 2 such that .beta.=0 and
for poxel 3 such that .gamma.=0. This yields:
S.sub.z'=R.sub.32S.sub.yR.sub.33S.sub.z, which yields S.sub.y; and
(15) S.sub.z''=V.sub.31S.sub.x+V.sub.32S.sub.y+V.sub.33S.sub.z,
which yields S.sub.x. (16)
Therefore, equations (11) to (16) give us S, with prior knowledge
of S, the star irradiance. Knowing S gives us the direction angles
to the star producing S.
Now, assume S is not known a priori. From equations (8) and
(10):
''' ##EQU00005##
Subtracting (18)-(17) yields:
'.function.'''.times..times..times..times..times..times..times.
##EQU00006##
Similarly for S.sub.z'':
.times..times..times..times..times..times..times..times..times..function.-
'''' ##EQU00007##
Since R.sub.31=0 (.beta.=0):
S.sub.z.sup.2=[R.sub.32S.sub.y+R.sub.33S.sub.z].sup.2+Term 1. (22)
S.sub.z.sup.2=R.sub.32.sup.2S.sub.y.sup.2+R.sub.33.sup.2S.sub.z.sup.2+2R.-
sub.32R.sub.33S.sub.yS.sub.z+Term 1 (23)
From equations (8) and (10):
##EQU00008## where i, j and k are an ordered triplet. So:
##EQU00009## which yields from (23) and (24):
.function..times..times..times..function..times..times..times.
##EQU00010##
This can be solved numerically to yield S.sub.z, where
S.sub.z>0, but may in general have two solutions. Now, from (21)
and since V.sub.32=0 (.gamma.=0):
S.sub.z.sup.2=[V.sub.31S.sub.x+V.sub.33S.sub.z].sup.2+Term 2
(27)
From (24) we have:
##EQU00011##
So:
.times..times..times..times..times..times..times..times..times..function.-
.times..times..times..times..times..times..times. ##EQU00012##
Now solve numerically for S.sub.z and pick a matching solution to
(26). Now S.sub.z is known. Now solve for S.sub.x.sup.2 and
S.sub.y.sup.2 using:
.times..times..times..times. ##EQU00013##
Then compute: S.sup.2=S.sub.x.sup.2+S.sub.y.sup.2+S.sub.z.sup.2
(32) to yield S, knowing S>0.
Now use (12) to get S.sub.z' which is >0.
Then use (15) to get S.sub.y.
Then use (13) to get S.sub.z'' which is >0.
Then use (16) to get S.sub.x.
Therefore, we have computed S with no prior knowledge of the star's
irradiance S.
Although star trackers that use navigational stars have been
described, other light-emitting or light-reflecting space objects
can be used for navigation. For example, most artificial satellites
have predictable orbits or other trajectories and can, therefore,
be used instead of, or in addition to, stars for navigation. This
concept was originally proposed by The Charles Stark Draper
Laboratory, Inc. and named Skymark. The star catalog 222 (FIG. 2)
can include ephemeris data about artificial satellites to
facilitate Skymark-type navigation using an embodiment of star
trackers disclosed herein.
A star tracker, as described herein, may be used in parallel with
another navigation system, such as a GPS, as a backup, in case an
on-board GPS receiver fails or the GPS is compromised. The star
tracker may be used to verify a GPS-determined position and take
over if the verification fails.
Although embodiments of the present invention have been described
in the contexts of star trackers, methods and apparatus described
herein may be used in other contexts, such as autocollimators or
other situations in which a need exists to measure an angle of
incidence.
While the invention is described through the above-described
exemplary embodiments, modifications to, and variations of, the
illustrated embodiments may be made without departing from the
inventive concepts disclosed herein. Furthermore, disclosed
aspects, or portions of these aspects, may be combined in ways not
listed above and/or not explicitly claimed. Accordingly, the
invention should not be viewed as being limited to the disclosed
embodiments.
Although aspects of embodiments may have been described with
reference to flowcharts and/or block diagrams, functions,
operations, decisions, etc. of all or a portion of each block, or a
combination of blocks, may be combined, separated into separate
operations or performed in other orders. All or a portion of each
block, or a combination of blocks, may be implemented as computer
program instructions (such as software, also referred to as
instruction codes or program codes), hardware (such as
combinatorial logic, Application Specific Integrated Circuits
(ASICs), Field-Programmable Gate Arrays (FPGAs) or other hardware),
firmware or combinations thereof.
Some embodiments have been described as including a
processor-driven controller. These and other embodiments may be
implemented by a processor executing, or controlled by,
instructions stored in a memory to perform functions described
herein. The memory may be random access memory (RAM), read-only
memory (ROM), flash memory or any other memory, or combination
thereof, suitable for storing control software or other
instructions and data. Instructions defining the functions of the
present invention may be delivered to a processor in many forms,
including, but not limited to, information permanently stored on
tangible non-writable storage media (e.g., read-only memory devices
within a computer, such as ROM, or devices readable by a computer
I/O attachment, such as CD-ROM or DVD disks), information alterably
stored on tangible writable storage media (e.g., floppy disks,
removable flash memory and hard drives) or information conveyed to
a computer through a communication medium, including wired or
wireless computer networks. Moreover, while embodiments may be
described in connection with various illustrative data structures,
systems may be embodied using a variety of data structures.
* * * * *
References